Debye_number

plasmapy.formulary.dimensionless.Debye_number(T_e: Quantity, n_e: Quantity) → Quantity

Return the number of electrons within a sphere with a radius of the Debye length.

Aliases: nD_

Parameters:

• T_e (Quantity) – Electron temperature.

• n_e (Quantity) – Electron number density.

Raises:

• TypeError – If either argument is not a Quantity.

• astropy.units.UnitConversionError – If either argument is in incorrect units.

• ValueError – If either argument contains invalid values.

Warns:

UnitsWarning – If units are not provided, SI units are assumed.

Returns:

N_D – Number of electrons within a sphere with a radius of the Debye length.

Return type:

Quantity

Notes

The Debye number is the number of electrons contained within a sphere with a radius of a Debye length and is given by

\[N_D = \frac{4π}{3} n_e λ_D^3\]

The Debye number is also known as the plasma parameter.

Collective behavior requires \(N_D ≫ 1\).

See also

Debye_length

Examples

>>> import astropy.units as u
>>> from astropy.constants.si import m_p, m_e
>>> Debye_number(5e6 * u.K, 5e9 * u.cm**-3)
<Quantity 2.17658...e+08>